Generative models that produce point clouds have emerged as a powerful tool
to represent 3D surfaces, and the best current ones rely on learning an
ensemble of parametric representations. Unfortunately, they offer no control
over the deformations of the surface patches that form the ensemble and thus
fail to prevent them from either overlapping or collapsing into single points
or lines. As a consequence, computing shape properties such as surface normals
and curvatures becomes difficult and unreliable.
In this paper, we show that we can exploit the inherent differentiability of
deep networks to leverage differential surface properties during training so as
to prevent patch collapse and strongly reduce patch overlap. Furthermore, this
lets us reliably compute quantities such as surface normals and curvatures. We
will demonstrate on several tasks that this yields more accurate surface
reconstructions than the state-of-the-art methods in terms of normals
estimation and amount of collapsed and overlapped patches.

本研究利用深度神经网络的可微分性，防止曲面崩溃和强烈减少曲面重叠，在表面重构方面显著超过现有技术。

通过学习可微分表面表示进行形状重建

Shape Reconstruction by Learning Differentiable Surface Representations

3D point cloud - a new signal representation of volumetric objects - is a
discrete collection of triples marking exterior object surface locations in 3D
space. Conventional imperfect acquisition processes of 3D point cloud - e.g.,
stereo-matching from multiple viewpoint images or depth data acquired directly
from active light sensors - imply non-negligible noise in the data. In this
paper, we adopt a previously proposed low-dimensional manifold model for the
surface patches in the point cloud and seek self-similar patches to denoise
them simultaneously using the patch manifold prior. Due to discrete
observations of the patches on the manifold, we approximate the manifold
dimension computation defined in the continuous domain with a patch-based graph
Laplacian regularizer and propose a new discrete patch distance measure to
quantify the similarity between two same-sized surface patches for graph
construction that is robust to noise. We show that our graph Laplacian
regularizer has a natural graph spectral interpretation, and has desirable
numerical stability properties via eigenanalysis. Extensive simulation results
show that our proposed denoising scheme can outperform state-of-the-art methods
in objective metrics and can better preserve visually salient structural
features like edges.

本文提出一种基于低维流形模型和图拉普拉斯正则化器的 3D 点云去噪方法，通过近似离散观测的流形维度计算，并且采用一种新的离散补丁距离度量来构建一个抗噪声的图形结构，并取得了比当前最先进方法更好的性能和更好的结构特征保持。

利用低维流形模型的图拉普拉斯正则化进行 3D 点云去噪

3D Point Cloud Denoising using Graph Laplacian Regularization of a Low  Dimensional Manifold Model

We propose a novel 3D shape parameterization by surface patches, that are
oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail
on local patches, we learn a patch dictionary that identifies principal surface
features of the shape. Unlike previous methods, we are able to encode surface
patches of variable size as determined by the user. We propose novel methods
for dictionary learning and patch reconstruction based on the query of a noisy
input patch with holes. We evaluate the patch dictionary towards various
applications in 3D shape inpainting, denoising and compression. Our method is
able to predict missing vertices and inpaint moderately sized holes. We
demonstrate a complete pipeline for reconstructing the 3D mesh from the patch
encoding. We validate our shape parameterization and reconstruction methods on
both synthetic shapes and real world scans. We show that our patch dictionary
performs successful shape completion of complicated surface textures.

通过表面贴片定义一种新颖的三维形状参数化方法，并提出了字典学习和贴片重建的新方法，在 3D 形状修补、去噪和压缩方面取得了好的效果。